I'm currently an A-level biologist and got stuck on the concept of 'introns.' I will try and lay out my question as logically as possible.
What I know: Triplets of bases code for an amino acid. There are 64 possible triplets. Taking away the 3 'stop' triplets, this leaves 61 combinations, all of which produce amino acids: some of the triplet combinations code for the same amino acid due to degenerate nature etc. During transcription of DNA to pre-mRNA we get a 'copy' (with uracil in place of thymine) of the gene's base sequence. In the process of splicing, introns (non-coding parts of the genetic code) are removed.

So my question is how AND why can introns be described as non-coding? Surely as all the triplets code amino acids, bar 3 'stop' triplets that signify the end of a gene, these should then be present in the protein/polypeptide. And, if they are amino acid coding, why are they present at all and how does the mechanism for splicing know to disregard these sections.

My idea was that the introns code for different smaller polypeptides which help with the formation of the 'main protein' that the gene codes for, but the amino acids that the triplets within the intron codes for are not included as part of the sequence of the main protein.

Introns are spliced out of the transcript before it leaves the nucleus and before translation (protein synthesis) begins. So we consider them 'non-coding' because they are (normally) never seen by the ribosomes and tRNAs. I say "normally" because there can be mutations at the intron/exon borders that can prevent splicing. In this case, the codons within the intron would indeed get translated into amino acids. The resulting protein would be non-functional because all of the amino acids after the mutation would be wrong. Also, many genes exhibit something called "alternative splicing" in which the same gene can be translated into more than one amino acid sequence by being spliced at different locations. For these genes, the splice variant that is expressed depends on things like, the cell type, the developmental period, environmental conditions, etc... In this case, the actual introns still do not get translated, but some sequences that would otherwise be treated as exons do get spliced out.